Important property for loop closure applications is rotational invariance, as the same place may be revisited from different directions.
Invariance to the viewpoint rotation translates into shift invariance along the angular direction of the scan image in polar coordinates.
To ensure this invariance we use a circular padding along the angular direction in all convolutions in the radar scan descriptor extraction network.
The left boundary of the scan image (corresponding to \(0^{\circ }\)  angular coordinate) is padded with values on the right boundary of the image (corresponding to \(360^{\circ }\)  angle) and vice verse.
This only partially solves the problem, as convolutions and pooling with stride 2 are not translational invariant due to the aliasing effect.
To mitigate this problem we augment the training data, by randomly rolling the image over axis corresponding to the angular direction, which gives the same effect as rotating an image in Cartesian coordinates.
Alternative approach is to apply anti-aliasing blurring [1]}, where stride 2 max-pooling and convolutions are replaced with stride 1 operations, followed by a stride 2 Gaussian blur. But we found it giving worse results in practice.
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